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There are two fuses in an electrical device. Let X denote

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 11SE Chapter 2

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 11SE

There are two fuses in an electrical device. Let X denote the lifetime of the first fuse, and let Y denote the lifetime of the second fuse (both in years). Assume the joint probability density function of X and Y is

\(f(x, y)= \begin{cases}\frac{1}{6} e^{-x / 2-y / 3} & x>0 \text { and } y>0 \\ 0 & \text { otherwise }\end{cases}\)

a. Find \(P(X \leq 2 \text { and } Y \leq 3)\).

b. Find the probability that both fuses last at least 3 years.

c. Find the marginal probability density function of X.

d. Find the marginal probability density function of Y .

e. Are X and Y independent? Explain.

Equation Transcription:

Text Transcription:

f(x,y)={_0     otherwise^{1over 6}e^{-x/2-y/3}     x>0 and y>0

P(X2 and Y3)

Step-by-Step Solution:

Solution:

Step 1 of 4 :

 There are two fuses in an electrical device . Let X denote the lifetime of the first fuse, and let Y denote the lifetime of the second fuse (both in years). And the joint probability density function of X and Y is

 

We have to find

  1.  P(X ≤ 2 and Y ≤ 3).
  2. The probability that both fuses last at least 3 years.

  1.   The marginal probability density function of X.

  1.   The marginal probability density function of Y.

  1.   Check X and Y are independent.

Step 2 of 4

Chapter 2, Problem 11SE is Solved
Step 3 of 4

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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There are two fuses in an electrical device. Let X denote